# Mathematics

## Instructions

Instructions: |

Week 5 Individual Assignment |

Total Number of Questions – 12 |

Total Points: 6 |

1. You have twelve problems – on each tab of this Excel file. |

2. Please show your work in the cells. Use Excel formulas instead of writing the values/answers directly in the cell. |

The instructor will then know where you made a mistake and provide you valuable feedback and partial credit (if appropriate). |

## Question 1

Find the interest paid on a loan of $1,200 for three years at a simple interest rate of 5% per year. |

How much money will you pay after three years? |

Principal |

Rate |

Time |

Simple Interest (SI) |

Maturity Value |

## Question 2

Find the maturity value of a loan of $1,750 for 28 months at 9.8% simple interest per year. | |

Principal | |

Rate | |

Time | — Please make sure that the time periods for Time and Rate match. |

Simple Interest (SI) | |

Maturity Value |

## Question 3

Find the simple interest rate of a loan of $5,000 that is made for three years and requires $1,762.50 in interest. |

Principal |

Time |

SI |

Rate |

## Question 4

A loan of $16,840 is borrowed at 9% simple interest and is |

repaid with $4,167.90 interest. What is the duration of the loan? |

Principal |

Rate |

SI |

Time |

## Question 5

How much money is borrowed if the interest rate is 9.25% simple interest |

and the loan is made for 3.5 years and has $904.88 interest? |

SI |

Rate |

Time |

Principal |

## Question 6

Find the ordinary and exact interest for a loan of $1000 at a 5% annual | |||

interest rate. The loan was made on March 15 and is due May 15. | |||

Loan date | Loan date | ||

Loan Due Date | Loan Due Date | ||

Exact time | days | Exact time | days |

Principal | Principal | ||

Rate | Rate | ||

Time | Time | ||

Ordinary Simple Interest (SI) | Exact Simple Interest (SI) |

## Question 7

Find the bank discount and proceeds using ordinary interest for a loan to Michelle Anders for $7,200 | |

at 8.25% annual simple interest from August 8 to November 8. | |

Loan date | |

Loan Due Date | |

Exact time | days |

Face Value (F) | |

Discount Rate (D) | |

Time Period (T) | years –> ‘Convert Exact time in days to years |

Bank Discount (B) | |

Proceeds (P) |

## Question 8

What is the effective interest rate of a simple discount note for $8,000, | |

at an ordinary bank discount rate of 11%, for 120 days? | |

Face Value (F) | |

Discount Rate (D) | |

Time Period (T) | years –> ‘Convert Exact time in days to years |

Bank Discount (B) | |

Proceeds (P) | |

Rate |

## Question 9

SOLVED EXAMPLE | ||

What is the effective interest rate for the ﬁrst year for a loan of $20,000 | ||

for three years if the interest is compounded quarterly at a rate of 12%? | ||

Quoted Rate | 12.00% | quarterly |

No. of compounding periods per year | 4 | For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 |

EAR | 12.55% | |

1. Ross Land has a loan of $8,500 compounded quarterly for four years at 6%. What is the effective interest rate for the ﬁrst year for the loan? | ||

Quoted Rate | ||

No. of compounding periods per year | For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 | |

EAR | ||

2. Find the effective interest rate for the ﬁrst year for a loan for four years compounded semiannually at an annual rate of 2% | ||

Quoted Rate | ||

No. of compounding periods per year | For Quarterly, type 4; for semiannually, type 2; for annually, type 1; for monthly, type 12; for daily, type 365 | |

EAR | ||

3. What is the effective interest rate for the ﬁrst year for a loan of $5,000 at 10% compounded daily for three years? | ||

Quoted Rate | ||

No. of compounding periods per year | ||

EAR | ||

4. Depending on the issuer, a typical credit card agreement quotes an interest rate of 18 percent APR. Monthly payments are required. | ||

What is the actual interest rate you pay on such a credit card? | ||

Quoted Rate | ||

No. of compounding periods per year | ||

EAR | =EFFECT(B30, B31) | |

5. Find the effective interest rate for a loan of $3,500 at 10% interest compounded quarterly. | ||

Quoted Rate | ||

No. of compounding periods per year | ||

EAR | =EFFECT(B36, B37) |

## Question 10

SOLVED EXAMPLE | ||

Tim Bowling has $20,000 invested for three years at a 5.25% annual rate compounded daily. | ||

How much interest will he earn? | ||

Initial Investment (PV) | $20,000 | |

Quoted Rate | 5.25% | |

Compounding Frequency | Daily | Choose one |

Number of compoundings (m) | 365 | |

Quoted Rate divided by m = RATE | 0.0144% | |

Number of Years | 3 | |

NPER (Num. of years * m) | 1095 | |

Ending Amount (FV) | $23,411.35 | |

Compound Interest | $3,411.35 | |

Exercise | ||

Find the future value of a $15,000 money market investment at 2.8% annual interest compounded daily for three years. | ||

Initial Investment (PV) | ||

Quoted Rate | ||

Compounding Frequency | ||

Number of compoundings (m) | ||

Quoted Rate divided by m = RATE | ||

Number of Years | ||

NPER (Num. of years * m) | ||

Ending Amount (FV) | ||

Compound Interest |

## Question 11

SOLVED EXAMPLE | ||

The Holiday Boutique would like to put away some of the holiday | ||

profits to save for a planned expansion. A total of $8,000 is needed in three years. How much | ||

money in a 5.2% three-year certificate of deposit that is compounded monthly must be invested | ||

now to have the $8,000 in three years? | ||

Future Value Needed (FV) | $8,000 | |

Quoted Rate | 5.2% | |

Compounding Frequency | Monthly | Choose one |

Number of compoundings (m) | 12 | |

Quoted Rate divided by m = RATE | 0.4333% | |

Number of Years | 3 | |

NPER (Num. of years * m) | 36 | |

Amount Invested Now (PV) | $6,846.78 | |

Exercise | ||

How much should be invested now to have $15,000 in six years if interest is 4% compounded quarterly? | ||

Future Value Needed (FV) | ||

Quoted Rate | ||

Compounding Frequency | ||

Number of compoundings (m) | ||

Quoted Rate divided by m = RATE | ||

Number of Years | ||

NPER (Num. of years * m) | ||

Amount Invested Now (PV) |

## Question 12

Jamie Juarez needs $12,000 in 10 years for her daughter’s college education. | |

How much must be invested today at 2% annual interest compounded | |

semiannually to have the needed funds? | |

Future Value Needed (FV) | |

Quoted Rate | |

Compounding Frequency | Choose one |

Number of compoundings (m) | |

Quoted Rate divided by m = RATE | |

Number of Years | |

NPER (Num. of years * m) | |

Amount Invested Now (PV) | |

A loan of $8,000 for two acres of woodland is compounded quarterly at an annual | |

rate of 6% for ﬁve years. Find the compound amount and the compound interest. | |

Initial Investment (PV) | |

Quoted Rate | |

Compounding Frequency | Choose one |

Number of compoundings (m) | |

Quoted Rate divided by m = RATE | |

Number of Years | |

NPER (Num. of years * m) | |

Ending Amount (FV) | |

Compound Interest |